Related papers: Geodesic connectedness of multiwarped spacetimes

The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…

We define the notion of geodesic completeness for semi-Riemannian metrics of low regularity in the framework of the geometric theory of generalized functions. We then show completeness of a wide class of impulsive gravitational wave…

A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and…

We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity…

We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional…

Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization…

We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral…

We give a covariant definition of closeness between (time oriented) Lorentzian metrics on a manifold M, using a family of functions which measure the difference in volume form on one hand and the difference in causal structure relative to a…

We suggest a construction that, given a trajectorial diffeomorphism between two Hamiltonian systems, produces integrals of them. As the main example we treat geodesic equivalence of metrics. We show that the existence of a non-trivially…

Building upon previous works characterizing GRW space-times using concircular and torse-forming vectors, this paper investigates a Lorentzian manifold equipped with a concircularly semi-symmetric metric connection. We demonstrate that such…

It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian…

Some well-known Lorentzian concepts are transferred into the more general setting of cone structures, which provide both the causality of the spacetime and the notion of cone geodesics without making use of any metric. Lightlike…

The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force…

This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…

The space ML(F) of measured geodesic laminations on a given closed hyperbolic surface F has a canonical linear structure arising in fact from different sources in 2-dimensional hyperbolic (earthquake theory) or complex projective (grafting)…

Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution homeomorphic to S^2 must contain an infinite number of…

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.

In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…

Helfer in [Pacific J. Math. 164/2 (1994), p. 321--350] was the first to produce an example of a spacelike Lorentzian geodesic with a continuum of conjugate points. In this paper we show the following result: given an interval $[a,b]$ of…

Semi-Riemannian manifolds that satisfy (homogeneous) linear differential conditions of arbitrary order on the curvature are analyzed. They include, in particular, the spaces with (higher-order) recurrent curvature, (higher-order) symmetric…